Q.Solve $\dfrac{2x-1}{3}\le \dfrac{x+2}{2}$ for $x\in\mathbb{R}$.

A linear inequation in one variable, $ax+b\ \square\ 0$ with $\square\in\{<,>,\le,\ge\}$, is solved like a linear equation with one extra rule: multiplying or dividing both sides by a negative number reverses the inequality sign ($<\leftrightarrow>$, $\le\leftrightarrow\ge$). Adding/subtracting or scaling by a positive number keeps the sign. The solution set is an interval — e.g. $x\le4$ is $(-\infty,4]$ — drawn on a number line with a closed dot for an included boundary ($\le,\ge$) and an open dot for an excluded one ($<,>$), s …